Ordered moments and relation to Radon transform of Wigner quasiprobability

Abstract

It is shown that the symmetrically ordered moments of boson operators for a single boson mode can be reconstructed from the corresponding moments of the Radon transform of the Wigner quasiprobability for discrete sets of equidistant inequivalent angles which solve the circle division problem. This reconstruction is sometimes simpler than the corresponding reconstruction of the normally ordered moments where one first has to multiply the Radon transform with Hermite polynomials in comparison to power functions for symmetrically ordered moments and then to integrate. The connection to the reconstruction for the general class of s-ordered moments is established. The transition from discrete sets of angles to integration over angles via averaging over the discrete angles is made. The results are applied to displaced squeezed thermal states. It is shown how the ordered moments for these states can be explicitly found from the calculated Radon transform of the Wigner quasiprobability. The obtained formulae for these moments possess independent interest since they contribute to the discussion of the properties of the most general class of states with quasiprobabilities of Gaussian form with many possible special cases as, for example, squeezed coherent states and squeezed thermal states.     

Modulation instability of light beam propagation near the supercollimation frequency in nonlinear photonic crystals

The modulation instability (MI) of light beam propagation near the supercollimation frequency in nonlinear photonic crystals was investigated. The role of the nonlinear diffraction effect, merged as a result of nonlinear tuning of the equal-frequency contour curvature, in MI is particularly identified. It is found that the nonlinear diffraction effect tends to stimulate or suppress MI depending on the sign of the product of nonlinear diffraction and Kerr effects. Further analysis reveals that the MI and soliton phenomenon may be steered by the tunable supercollimation frequency in nonlinear photonic crystals.     

Polarization-dependent angle filters based on one-dimensional photonic crystals using mu-negative materials

We study transmission properties of one-dimensional photonic crystals consisting of mu-negative and positive index materials by using transfer matrix methods. The results show that transmission properties of the transverse electric waves depend on permittivity (?), while transmission properties of the transverse magnetic waves depend on permeability (μ); there exists a transmission band inside the single-negative gap in this periodic structure without defects, and the transmission band is insensitive to the incident angle for the transverse electric waves but sensitive for the transverse magnetic waves. This property can be used to make polarization-dependent angle filters.     

General conditions of polarization-independent transmissions in one-dimensional magnetic photonic crystals

Abstract

Based on the transfer matrix theory, general conditions of polarization-independent transmissions in one-dimensional photonic crystals are derived. It is shown that the polarization-independent transmissions are obtained in photonic crystals consisting of two alternating layers with the same refraction index and optical thickness as well as the mutually reciprocal wave impedance. By using two different photonic crystals satisfying the above relation to constitute the light quantum-well structures, the structures have polarization-independent transmission properties. When a defective layer with wave impedance of 1 is introduced in the photonic crystals, the defective photonic crystals also have the polarization-independent transmission properties. In addition, polarization-independent low-pass spatial filters are achieved based on these photonic crystal structures.     

Selective excitation of LP01 mode in multimode fiber using solid-core photonic crystal fiber

To address the overwhelming bandwidth increase in premise backbones, an attractive alternative for selective mode excitation in multimode fiber (MMF) using solid-core photonic crystal fiber (PCF) is presented. The power coupling efficiency, differential mode delay, and bit-error rate performance of several structural designs of solid-core PCF waveguides are investigated for the selective excitation of mode LP01 in a MMF. The achieved coupling efficiency into mode LP01 is above 90% for PCF profiles with seven rings.     

Observation of electromagnetically induced photonic band gaps in hot two-level atoms

In this paper, two-level thermal Cs atoms are used to observe electromagnetically induced photonic band gaps with a strong symmetric and two types of asymmetric standing-wave (SW) driving fields. One main band and two sidebands are measured for the transmitted and reflected spectra. We carry out physical interpretation about the observations in SW-dressed atom picture and employ method of Fourier transformation to solve density-matrix equations for hot two-level system to simulate the experimental results. The numerical analyses are consistent with the experimental observations for properties of electromagnetically induced photonic band gaps.     

Low-power optical switching with Kerr nonlinear material in two-dimensional photonic crystal nanocavity

We investigate numerically optical bistability in direct-coupled cavity–waveguide photonic crystal system using the finite-difference time-domain method. The quality factor of the cavity is optimized by engineering the geometrical parameters. Numerical results indicate that the threshold power of optical bistability can be reduced greatly due to the increased quality factor.     

Design of ultra-low and ultra-flattened dispersion single mode photonic crystal fiber by DE/EDA algorithm

This paper proposes a combination of differential evolution (DE) and estimation of distribution algorithm (EDA) to design photonic crystal fiber structures with desired properties over the C communication band. In order to determine the effective index of propagation of the mode and then, the other properties of structure, a finite difference frequency domain (FDFD) solver is applied. The results revealed that the proposed method is a powerful tool for solving this optimization problem. The optimized PCF exhibits a dispersion of 0.22 ps nm^?1 km^?1 at 1.55 µm wavelength with a variance of ±0.4 ps nm^?1 km^?1 over the C communication band and a nearly zero dispersion slope.     

Fictitious Rayleigh expansions

Scattering matrix and transfer matrix methods are widely used in the frame of scattering from a stack of thin films, a stack of periodic grids or photonic crystals. They allow one to reduce significantly computation time and memory storage. However, these methods have well-known theoretical limits since they require the field to take the form of plane wave expansions (Rayleigh expansions) on both sides of each element of the stack. It will be shown that, in fact, the domain of validity of these methods can be considerably extended by defining fictitious Rayleigh expansions between two consecutive elements, even when they are not separated by a homogeneous region. Numerical results confirm this prediction.